The subject of this thesis is the simulation study of the development of extensive air show ers produced by very high energy gamma-ray and hadronic cosmic rays with respect to the Cherenkov light they produce, and its imaging in ground based telescopes. Chapters 1-4 are introductory: Chapter 1 covers the mechanisms responsible for the production of very high energy gamma-rays, whereas, chapter 2 focusses on the development of extensive air showers and Cherenkov light production. Chapter 3 covers the instrumentation used to measure the Cherenkov light using the imaging atmospheric Cherenkov technique. Chapter 4 covers known and possible sources of very high energy gamma-rays. Chapters 5, 6 and 7 cover research performed by the author: Chapter 5 discusses some of the differences between three popular extensive air shower simulations codes, namely ALTAI, CORSIKA and MOCCA. Chapter 6 details the simulation of the response of two ground based imaging atmospheric Cherenkov telescope (the Durham Mark 6 and stand-alone H.E.S.S. telescopes), and in particular details the derivation of the flux of the x-ray selected BL-LAC PKS 2155-304 with the Durham Mark 6 telescope. This represents the refinement of a published measurement given an improved telescope simulation. The significance of the signal seen is 6.8o, and the integral flux derived above 1.5 TeV (assuming a differential spectral slope of-2.6) is {2.5±0.7stat ± (^0.5)(_1.6syst) x 10(^-7) photons m(^-2) s(^-1) Chapter 7 discusses the importance of the atmosphere, and the results of shower simulations under different atmospheric assumptions are presented, which indicate the importance of atmospheric calibration for the new generation of Cherenkov telescopes. The results of this chapter suggest that to first order large changes in the low level aerosol concentration have a much more significant effect on the trigger rate of a stand-alone H.E.S.S. telescope, than on the Hillas parameter distributions seen. Chapter 8 brings together the work done in this thesis, and highlights a final set of fluxes for the active galactic nuclei sources seen with the Durham Mark 6 telescope, many of which will form future sources to be measured with the H.E.S.S. system. The current status of the stand-alone H.E.S.S. system is also covered in chapter 8. The thesis concludes with a further brief discussion of the future prospects for imaging atmospheric Cherenkov astronomy.